Green functions in metric measure spaces

一、报告题目 Green functions in metric measure spaces 二、主讲人 Xiaodan Zhou（日本冲绳科学技术大学） 三、报告时间 2023年10月20日 15:00-16:00 四、报告地点 腾讯会议：546-172-078 五、摘要 In Euclidean space Rn, a result of Kichenassamy and Veron shows that the n-Laplace operator admits a unique global Green function, i.e., there is a unique, properly normalized singular solution which blows up to +∞at the origin and converges to −∞at infinity. Their proof of uniqueness includes the p-Laplacian Lp in the range 1 < p≤n and is based on C1,αestimates for p-harmonic functions. The argument was later simplified and extended to the Riemannian and Carnot group setting, and thus establishing uniqueness of Green functions in the conformal case p = n in these geometries. The purpose of this talk is to extend this uniqueness result to the setting of complete metric spaces (X, d, μ) equipped with an Ahlfors regular Borel measure μ, and a Poincare inequality. This is a joint work with Mario Bonk and Luca Capogna. 六、主讲人简介 Xiaodan Zhou, 2011年本科毕业于北京师范大学，2016年博士毕业于美国匹兹堡大学，导师为Pitro Hajlasz教授，现为日本冲绳科学技术大学助理教授，度量空间上的分析团队负责人。主要研究方向为奇异度量空间上的分析，特别是次黎曼流形上的分析，在Cal. Var. PDEs, Int. Math. Res. Not., Ann. Sc. Norm. Super. Pisa, Indianda Univ. Math. J.等国际高水平期刊发表论文10余篇。 七、主办单位 非线性期望前沿科学中心 数学与交叉科学研究中心 中俄数学中心青岛基地